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Mathematics
Mathematics
Problem
Consider the system
d
x
d
t
=
3
y
,
d
y
d
t
=
−
2
x
\frac{dx}{dt}=3y, \qquad \frac{dy}{dt}=-2x
d
t
d
x
=
3
y
,
d
t
d
y
=
−
2
x
with initial conditions
x
(
0
)
=
4
x(0)=4
x
(
0
)
=
4
and
y
(
0
)
=
1
y(0)=1
y
(
0
)
=
1
. What is the value of
d
2
x
d
t
2
\dfrac{d^{2}x}{dt^{2}}
d
t
2
d
2
x
at
t
=
0
t=0
t
=
0
? a)
−
8
-8
−
8
b)
24
24
24
c)
−
24
-24
−
24
d)
−
6
-6
−
6
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